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(a) Consider the vector field ^ F(x, y, z)-(e* sin y-yz) + (e* cos y-xz) j + (z-xy)k. (i) Show that the vector field F is conservative (ii) Determine the potential function f(x,y,:) for the vector field F. ii) Hence, or otherwise, evaluate the work done by the vector field F along the line segment from the point (1 , 0, 1 ) to the point (2.-1) (7 marks)

(b) Consider the solid region D bounded by y 0,z 0,yx and z 2-x. Sketch the region D in the xyz-space, and evaluate the triple integral (10 marks)


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